Fundamental Concepts

GSP views genetic sequences as signals that can be analyzed using various signal processing methods. This perspective is rooted in the observation that genetic sequences can exhibit regularities and patterns similar to those found in traditional signals. The primary steps involve:

1. Representation: For instance, in the case of a DNA sequence, the four nucleotides (A, C, G, T) can be represented as complex numbers or vectors. This numerical representation of the sequence allows for the application of signal processing techniques.
2. Transformation: An example of a transformation technique used in GSP is the Fourier Transform. This technique transforms the genetic sequence from the time (or spatial) domain to the frequency domain, highlighting the periodic components of the genetic sequence. Other techniques like Wavelet Transform can also be used, which provide time-frequency representation of the signal.
3. Interpretation: The interpretation stage is where the results of the transformation are related back to biological information. For instance, a peak in the frequency domain may correspond to a repeating pattern in the genetic sequence, which could be indicative of a certain genetic feature or mutation. This could potentially be used for detecting genetic diseases or abnormalities.

Examples

1. Representation

In a study conducted on the Human Genome Project, the researchers had to represent the DNA sequence in a way that was compatible with signal processing techniques. They chose to represent each nucleotide (A, C, G, T) as a unique complex number. For instance, they used the following mapping: A = 1, C = -1, G = i, T = -i. With this numerical representation, they were able to process the genetic sequence as a signal.

2. Transformation

In another study on the same Human Genome Project, the researchers decided to use the Fourier Transform to transform the genetic sequence from the time domain to the frequency domain. The transformed sequence revealed peaks at certain frequencies, indicating the presence of repeating patterns in the genetic sequence.

3. Interpretation

Upon observing the peaks in the frequency domain, the researchers had to interpret what these peaks meant in a biological context. They determined that these peaks corresponded to repeating sequences of nucleotides in the genome, also known as tandem repeats. These tandem repeats are known to play a crucial role in genomic diseases and evolution. Hence, the researchers were able to link their signal processing analysis back to significant biological findings.